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- Butterfly_diagram abstract "This article is about butterfly diagrams in FFT algorithms; for the sunspot diagrams of the same name, see Solar cycle. In the context of fast Fourier transform algorithms, a butterfly is a portion of the computation that combines the results of smaller discrete Fourier transforms (DFTs) into a larger DFT, or vice versa (breaking a larger DFT up into subtransforms). The name \"butterfly\" comes from the shape of the data-flow diagram in the radix-2 case, as described below. The earliest occurrence in print of the term is thought to be in a 1969 MIT technical report. The same structure can also be found in the Viterbi algorithm, used for finding the most likely sequence of hidden states.Most commonly, the term \"butterfly\" appears in the context of the Cooley–Tukey FFT algorithm, which recursively breaks down a DFT of composite size n = rm into r smaller transforms of size m where r is the \"radix\" of the transform. These smaller DFTs are then combined via size-r butterflies, which themselves are DFTs of size r (performed m times on corresponding outputs of the sub-transforms) pre-multiplied by roots of unity (known as twiddle factors). (This is the \"decimation in time\" case; one can also perform the steps in reverse, known as \"decimation in frequency\", where the butterflies come first and are post-multiplied by twiddle factors. See also the Cooley–Tukey FFT article.)".
- Butterfly_diagram thumbnail Butterfly-FFT.png?width=300.
- Butterfly_diagram wikiPageExternalLink fft.html.
- Butterfly_diagram wikiPageExternalLink fft.html.
- Butterfly_diagram wikiPageID "2707212".
- Butterfly_diagram wikiPageLength "5718".
- Butterfly_diagram wikiPageOutDegree "20".
- Butterfly_diagram wikiPageRevisionID "706867074".
- Butterfly_diagram wikiPageWikiLink Butterfly.
- Butterfly_diagram wikiPageWikiLink Category:Diagrams.
- Butterfly_diagram wikiPageWikiLink Category:FFT_algorithms.
- Butterfly_diagram wikiPageWikiLink Composite_number.
- Butterfly_diagram wikiPageWikiLink Cooley–Tukey_FFT_algorithm.
- Butterfly_diagram wikiPageWikiLink Discrete_Fourier_transform.
- Butterfly_diagram wikiPageWikiLink Fast_Fourier_transform.
- Butterfly_diagram wikiPageWikiLink Massachusetts_Institute_of_Technology.
- Butterfly_diagram wikiPageWikiLink Mathematical_diagram.
- Butterfly_diagram wikiPageWikiLink Recursion.
- Butterfly_diagram wikiPageWikiLink Root_of_unity.
- Butterfly_diagram wikiPageWikiLink Signal-flow_graph.
- Butterfly_diagram wikiPageWikiLink Solar_cycle.
- Butterfly_diagram wikiPageWikiLink Twiddle_factor.
- Butterfly_diagram wikiPageWikiLink Viterbi_algorithm.
- Butterfly_diagram wikiPageWikiLink Zassenhaus_lemma.
- Butterfly_diagram wikiPageWikiLink File:Butterfly-FFT.png.
- Butterfly_diagram wikiPageWikiLink File:DIT-FFT-butterfly.png.
- Butterfly_diagram wikiPageWikiLinkText "Butterfly diagram".
- Butterfly_diagram wikiPageWikiLinkText "butterflies".
- Butterfly_diagram wikiPageWikiLinkText "butterfly diagram".
- Butterfly_diagram wikiPageWikiLinkText "butterfly".
- Butterfly_diagram subject Category:Diagrams.
- Butterfly_diagram subject Category:FFT_algorithms.
- Butterfly_diagram type Algorithm.
- Butterfly_diagram type Infographic.
- Butterfly_diagram type Transform.
- Butterfly_diagram comment "This article is about butterfly diagrams in FFT algorithms; for the sunspot diagrams of the same name, see Solar cycle. In the context of fast Fourier transform algorithms, a butterfly is a portion of the computation that combines the results of smaller discrete Fourier transforms (DFTs) into a larger DFT, or vice versa (breaking a larger DFT up into subtransforms). The name \"butterfly\" comes from the shape of the data-flow diagram in the radix-2 case, as described below.".
- Butterfly_diagram label "Butterfly diagram".
- Butterfly_diagram sameAs Q1529451.
- Butterfly_diagram sameAs Schmetterlingsgraph.
- Butterfly_diagram sameAs m.07z8bb.
- Butterfly_diagram sameAs Бабочка_(БПФ).
- Butterfly_diagram sameAs Q1529451.
- Butterfly_diagram wasDerivedFrom Butterfly_diagram?oldid=706867074.
- Butterfly_diagram depiction Butterfly-FFT.png.
- Butterfly_diagram isPrimaryTopicOf Butterfly_diagram.
